# 中位數

## 公式

${\displaystyle \mathrm {Q} _{\frac {1}{2}}(x)={\begin{cases}x'_{\frac {n+1}{2}},&{\mbox{if }}n{\mbox{ is odd number.}}\\{\frac {1}{2}}(x'_{\frac {n}{2}}+x'_{{\frac {n}{2}}+1}),&{\mbox{if }}n{\mbox{ is even number.}}\end{cases}}}$

## 中位數特性

### 常態分配下的中位數

k(n)和n的對應表
n k(n) n k(n) n k(n)
2 0.500267128 70 0.021985179 138 0.011271806
3 0.448703237 71 0.021403637 139 0.011269587
4 0.298172500 72 0.021393271 140 0.011109049
5 0.286770401 73 0.020840845 141 0.011111745
6 0.214713620 74 0.020830427 142 0.010959968
7 0.210476952 75 0.020295864 143 0.010962027
8 0.168172011 76 0.020294599 144 0.010810205
9 0.166171644 77 0.019776971 145 0.010809127
10 0.138304145 78 0.019777466 146 0.010661452
11 0.137221972 79 0.019291777 147 0.010659591
12 0.117603985 80 0.019294767 148 0.010513172
13 0.116875871 81 0.018831955 149 0.010523498
14 0.102209683 82 0.018826854 150 0.010377973
15 0.101704592 83 0.018394657 151 0.010379735
16 0.090397468 84 0.018390467 152 0.010244606
17 0.090046842 85 0.017972657 153 0.010247290
18 0.081017991 86 0.017972309 154 0.010109136
19 0.080776427 87 0.017567447 155 0.010114347
20 0.073450103 88 0.017564340 156 0.009986419
21 0.073284584 89 0.017187295 157 0.009984465
22 0.067168338 90 0.017189110 158 0.009862704
23 0.067002164 91 0.016812903 159 0.009858886
24 0.061881619 92 0.016813666 160 0.009735345
25 0.061762647 93 0.016466660 161 0.009736185
26 0.057309720 94 0.016462668 162 0.009617128
27 0.057271174 95 0.016125488 163 0.009619325
28 0.053440064 96 0.016119237 164 0.009501480
29 0.053332370 97 0.015802880 165 0.009502525
30 0.049992614 98 0.015797856 166 0.009389839
31 0.049937448 99 0.015492872 167 0.009388423
32 0.047029351 100 0.015490432 168 0.009279058
33 0.046965211 101 0.015190773 169 0.009277712
34 0.044337988 102 0.015189776 170 0.009169514
35 0.044336558 103 0.014904567 171 0.009169768
36 0.041990927 104 0.014896640 172 0.009061071
37 0.041942218 105 0.014628725 173 0.009060657
38 0.039852927 106 0.014623638 174 0.008961003
39 0.039832458 107 0.014359452 175 0.008957769
40 0.037939073 108 0.014359166 176 0.008860612
41 0.037904745 109 0.014100614 177 0.008859363
42 0.036184274 110 0.014104129 178 0.008762802
43 0.036152192 111 0.013856818 179 0.008760489
44 0.034579591 112 0.013854712 180 0.008665028
45 0.034577569 113 0.013609600 181 0.008663662
46 0.033133177 114 0.013610680 182 0.008571695
47 0.033118807 115 0.013383360 183 0.008570240
48 0.031791145 116 0.013382329 184 0.008475410
49 0.031783399 117 0.013153728 185 0.008477845
50 0.030548873 118 0.013156167 186 0.008388634
51 0.030533811 119 0.012938560 187 0.008384818
52 0.029411882 120 0.012939455 188 0.008300454
53 0.029402885 121 0.012729706 189 0.008300175
54 0.028347691 122 0.012731381 190 0.008214157
55 0.028342062 123 0.012533040 191 0.008211878
56 0.027348747 124 0.012525181 192 0.008130539
57 0.027350473 125 0.012333899 193 0.008128310
58 0.026442809 126 0.012334408 194 0.008045347
59 0.026436289 127 0.012141084 195 0.008041810
60 0.025573242 128 0.012138522 196 0.007964784
61 0.025575279 129 0.011964057 197 0.007961234
62 0.024780610 130 0.011961887 198 0.007882679
63 0.024751923 131 0.011782874 199 0.007882009
64 0.024005574 132 0.011779941 200 0.007806200
65 0.024006688 133 0.011604216 201 0.007801090
66 0.023304209 134 0.011600908 202 0.007729016
67 0.023287460 135 0.011433315 203 0.007728333
68 0.022616908 136 0.011438587 204 0.007654504
69 0.022624425 137 0.011271806 205 0.007652196

1. 樣本個數為偶數，迴歸式為k(n) = 0.0000148965 + 1.5599936862 / n。

2. 樣本個數為奇數，迴歸式為k(n) = 0.0000084608 + 1.5674001064 / n。